In this section we show an analysis similar to that from Section REF  in the main text, but here we choose \(m_1=m_2=2\) . We begin with a simulation: We generate \(N=100\)  datasets assuming that the models specified in \(H_0^{(I)}\)  and \(H_0^{(G)}\)  are correct. Figure REF  shows the squared Hellinger distances of the estimates to the closest Laguerre type densities with \(m_1=m_2=2\) . The vertical lines show the distances which are obtained from the real data set. In case of the incubation period \(60\%\)  of the simulated distances are larger, for the generation time this percentage is lower, \(21\%\) , but still high. Finally, both distances are simultaneously larger for both densities in \(14\%\)  of the simulated cases. Thus, we conclude that also in this larger model class there is no evidence in the dataset which would contradict the parametric models fitted by [1]} and [2]}.
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